Few people can have experienced anything like what Barack Obama experienced on Tuesday. Things are running late, you're shuffled quickly through white marbled corridors, hands are shaken, cameras twitch and flash. Then suddenly the cold winter sunshine is on your face and you're gazing down at an ocean of people staring only at you.

Sitting on my sofa, I undoubtedly had the better view than the two million-strong crowd gathered along the Mall. Every defiant gesture, every look of brief uncertainty, and the delightful sight of the new president's daughter filming his speech for posterity on her camera was caught on TV. Yet, of course, it was not the quality of the experience that was important, but the act of being present that mattered to those who flooded Washington.

Those crowds proved that, despite the unrelenting pace of technological progress, the simple act of being present is still what's most important to us. All the twittering, webcasts and hi-definition live feeds are no replacement for your flesh and blood presence. Neither do they compete with being able to say, as so many people interviewed explained, that you were there – a witness and a participant, feeling like the event belonged to you.

It's a reassuring thought: if all the theatres in the West End finally fall down, if we can have a perfect live holographic projection of Dame Vanessa Redgrave on every stage in the country, if the Arts Council is only left with two copies of The Empty Space and a box of Cadbury's Roses to distribute to the starving artists of England, people will still want to gather together and be a part of something.

Yet increasingly I also find myself fascinated by the complete opposite – by the act of not being present. Can theatre still happen if nobody is there to see it? Can it exist only in the imagination? For me, theatre is more a process than a product – something that's happening rather than something that exists independently from people's experience of it. With this in mind, is there any reason why theatre can't be something that happens purely in our heads?

One show that I look to for inspiration, that has enthralled me more than almost any other is Forced Entertainment's Nights in This City – and yet I've never actually had the chance to experience it. I've followed its unsettling, disorientating journey through the streets of Sheffield in my head; played out its fractured relationship between the real city and the stories the audience are told of it so many times. This imaginary idea continues to fuel so much of what I do, forging itself a presence in the real world more powerful than many shows I've actually seen.

The next question has to be, then, can a theatre that exists only in our heads ever be shared; can it ever bring people together? Potentially. In his brilliant book, Moondust, Andrew Smith describes the Apollo space programme as the greatest piece of theatre the world has ever seen: a magnificent performance by 20 actors and thousands of backroom staff. Yet that performance was experienced by no one bar the performers. It didn't exist in the grainy black and white footage, the radio broadcasts, the transcripts or in the endless news coverage. It existed most powerfully as an idea, a dream of travelling out into the emptiness of space and gazing back at the world. And for a brief time, that was an idea that the entire world shared in.